Sensitivity analysis is an integral part of mathematical modelling, and in particular a crucial element of decision making in presence of uncertainties. The Fisher information, first introduced by Fisher [1]} and is widely used for parameter estimation and statistical inference, has found increasing application in many area of science and engineering for probabilistic sensitivity analysis. For example, the Fisher Information Matrix (FIM) has been applied to the parametric sensitivity study of stochastic biological systems [2]}; the FIM is used to study sensitivity, robustness, and parameter identifiability in stochastic chemical kinetics models [3]}; through link with relative entropy, the Fisher information is used to assess the most sensitive directions for climate change given a model for the present climate [4]}; used in conjunction with the principle of Max Entropy, the FIM is used to identify the pivotal voters that could perturb the collective voting outcomes in social systems [5]}; and more recently in [6]} the Fisher information have been proposed as one of the process-tailored sensitivity metrics for engineering design. Despite the wide scope, the applications mentioned above all utilise the spectral analysis of the FIM, i.e., the eigenvalues and eigenvectors of the FIM reveal the most and least sensitive directions of the system.
